"I think the White House should apologize and fire her. I think the remarks are disgusting. It's depressing, Craig, when you hear that kind of talk when you look at the service of Sen. McCain," Costello told CBS News host Craig Melvin.

"As a party, I think we need to do a better job of getting out in front of this stuff quickly, condemning it, and saying it has no place in our discourse," Costello added.